Conventionally, a method for applying a mean filter or a median filter to a whole of an image is well known as a noise reduction method for reducing a noise, which is overlapped on the image obtained by projecting a real space to a plane having multiple picture cells.
When the mean filter is applied to the image, a Gaussian noise is reduced. When the median filter is applied to the image, an impulse noise is reduced. However, when these methods are applied to the image, a whole of the image is averaged. Thus, an edge component in the image may be blurred. Specifically, when the mean filter or the median filter is applied to the image, a high frequency component showing a fine structure of an object projected to the image may not remain.
In order to preserve the high frequency component, a method with using a ε-filter is proposed. The ε-filter is prepared by modifying the mean filter. In order to preserve the high frequency component, a method for synthesizing a corrected image filtered through the mean filter and an original image with a ratio corresponding to an edge characteristic value indicative of the degree of the edge is proposed. These methods are described in, for example, JP-A-2010-92461 corresponding to US 2010/0066868.
The ε-filter preserves a picture cell value of each picture cell in a masking area when the difference of the picture cell value between the picture cell and the focused picture cell is small. The ε-filter replaces a picture cell value of each picture cell with the picture cell value of the focused picture cell when the difference of the picture cell value between the picture cell and the focused picture cell is large. Then, the image is averaged with using the picture cell value of each picture cell, i.e., the image is averaged with using only the picture cell value of the picture cell having the picture cell value smaller than the focused picture cell. Thus, when the noise of the mage is reduced with using the ε-filter, the noise is not reduced when the picture cell value of the picture cell providing the edge is not larger than the picture cell value of the noise component. Further, the ε-filter does not reduce the impulse noise.
In the noise reduction method described in JP-A-2010-92461, firstly, the median filter filters the image, on which a noise is overlapped, so that pre noise-reduction image is generated. Then, the edge characteristic value of the pre noise-reduction image is retrieved from a ratio between a dispersion value of a signal level in arrange including the focused picture cell and the dispersion value of the signal level of a whole of the pre noise-reduction image.
However, in the noise reduction method in JP-A-2010-92461, since the pre noise-reduction image is obtained with using the median filter, the edge characteristic value is not calculated with high accuracy. Thus, the fine structure of the object projected as the image is not clear.
Thus, the above methods do not provide the sufficient reduction of the noise, which overlaps on the image.
In order to reduce the noise sufficiently, another method for reducing the noise is proposed in JP-A-2008-172431 corresponding to US 2009/0324066. In the method, an image signal for providing the image is divided into a first signal component and a second signal component. A noise reduction parameter, which is necessary for the noise reduction process, is prepared according to the signal level of the first signal component. Then, the noise in the second signal component is reduced. Here, the first signal component represents a framework component of the object, which is projected to the image. The first signal component includes the edge component. Further, the second signal component represents a residual error of the first signal component with respect to the image signal.
In the method described in JP-A-2008-172431, a parameter is necessary when the image signal is divided into the first and second signal components. The parameter is referred as a dividing parameter. The dividing parameter is introduced by solving a formulated energy functional with a Projection method. Here, the energy functional is formulated by minimizing the energy functional as a variational problem.
In the above method in JP-A-2008-172431, although the noise overlapping the image is reduced, a throughput for determining an optimum value of the dividing parameter is large.